I tested this in Linux Mint 14. I’m using jdk-7u1 as an example. Modify as needed.

First, download your desired version of the JDK for Linux from the Oracle site.

Extract it:

tar -xvf jdk-7u1-linux-x64.tar.gz

Move it to the jdk folder:

sudo mv ./jdk1.7.0_01 /usr/lib/jvm/jdk1.7.0_01

Install the new jvm into the java link group:

sudo update-alternatives --install /usr/bin/java java /usr/lib/jvm/jdk1.7.0_01/bin/java 1

Now, when you choose your default Java, the new jdk will be one of the options:

sudo update-alternatives --config java